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A source of light and a screen are place...

A source of light and a screen are placed 90 cm apart. Where should a convex lens of 20 cm focal length be placed in order to form a real image of the source on the screen ?

A

30 cm or 60 cm

B

20 cm or 70 cm

C

40 cm or 50 cm

D

35 cm or 65 cm

Text Solution

Verified by Experts

The correct Answer is:
A

For the lens, `u=-u, v=(90-u)` +ve and `f=+20 cm`
`because (1)/(v)-(1)/(u)=(1)/(20) therefore (1)/(90-u)-((1)/(-u))=(1)/(20)`
`therefore (1)/(90-u) +(1)/(u)=(1)/(20) therefore (u+90-u)/(u(90-u))=(1)/(20)`
`therefore (90)/(90u-u^(2))=(1)/(20)`
` therefore 90u-u^(2)=1800 therefore u^(2)-90u=-1800`
` therefore u^(2)-90u+1800=0 therefore (u-30)(u-60)=0`
`therefore u=30 cm or u=60 cm`
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